To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $p-2q$ and $p+2q$ is $\left(p-2q\right)\left(p+2q\right)$. Multiply $\frac{2}{p-2q}$ times $\frac{p+2q}{p+2q}$. Multiply $\frac{1}{p+2q}$ times $\frac{p-2q}{p-2q}$.
Since $\frac{2\left(p+2q\right)}{\left(p-2q\right)\left(p+2q\right)}$ and $\frac{p-2q}{\left(p-2q\right)\left(p+2q\right)}$ have the same denominator, add them by adding their numerators.
